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  4. Three long straight conductors are arranged parallel to each other in the same plane. They carry currents of 1A , 2A and 3A in the same direction. The distance between the first two conductors is x and the distance between the second and third conductors is y . If the middle conductor is in equilibrium, then the ratio x:y is

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Q. Three long straight conductors are arranged parallel to each other in the same plane. They carry currents of $1A$ , $2A$ and $3A$ in the same direction. The distance between the first two conductors is $x$ and the distance between the second and third conductors is $y$ . If the middle conductor is in equilibrium, then the ratio $x:y$ is

NTA AbhyasNTA Abhyas 2022

Solution:

Force per unit length between two current carrying parallel wire is given by :
$F=\frac{\mu _{0} i_{1} i_{2}}{2 \pi r}$ &
$f_{12}+f_{23}=0$
$\frac{\mu _{o} 1 \times 2}{2 \pi \, x}=\frac{\mu _{o} 2 \times 3}{2 \pi y} \\ \frac{x}{y}=\frac{1}{3}$